Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 29
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Trying to find an order 29 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
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Ending with final polynomial:
P : 35/8*t^33 - 5136614102002674555/145922366335413044*t^31 + 23489302772876510428914/182950166793024103915*t^29 - 205470359692791334556723/731800667172096415660*t^27 + 28869993935188730840817/70365448766547732275*t^25 - 4791533383639736875742643/11337281105266170624148*t^23 + 15202396530748375874687223/48183444697381225152629*t^21 - 33306571312415996602079061/192733778789524900610516*t^19 + 232012469243114769892987953/3337337537987036436887356*t^17 - 19986048041843322367078623/981569864113834246143340*t^15 + 1283911486125352447869792/301482172549249089886883*t^13 - 30447924914546920839484881/49443076298076850741448812*t^11 + 17635624827095856778098/301482172549249089886883*t^9 - 3137219380412395192827/932888232039185863046204*t^7 + 3020751317479003365052521/29727649624218706508296098215*t^5 - 202129707657203363082519/166474837895624756446458150004*t^3 + 796866948412365610971/332949675791249512892916300008*t
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Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.98832819179765564205 + 3.6683011280439871691e-436j)  +/-  (1.05e-116, 1.05e-116j)
| (-1.4267811809247537089e-451 - 2.1099914440953179231e-451j)  +/-  (8.41e-450, 8.41e-450j)
| (-0.86113631159405257522 - 9.8927360847070750967e-446j)  +/-  (1.5e-117, 1.5e-117j)
| (-0.94290042454780854051 - 1.8268457615698606199e-445j)  +/-  (8.21e-117, 8.21e-117j)
| (0.94290042454780854051 + 4.0648479085266004435e-444j)  +/-  (7.48e-117, 7.48e-117j)
| (0.90647250194602471442 + 8.6582420860336538293e-449j)  +/-  (3.82e-117, 3.82e-117j)
| (-0.98832819179765564205 + 7.8424837974331618233e-451j)  +/-  (1.05e-116, 1.05e-116j)
| (-0.90647250194602471442 - 1.6908601209039540196e-451j)  +/-  (3.56e-117, 3.56e-117j)
| (-0.99786320427767492839 - 4.3769465291918507531e-451j)  +/-  (4.11e-117, 4.11e-117j)
| (0.99786320427767492839 + 9.8343145415549028999e-451j)  +/-  (3.94e-117, 3.94e-117j)
| (0.86113631159405257522 + 9.9747172461719035431e-458j)  +/-  (1.51e-117, 1.51e-117j)
| (0.97017665850723381607 - 5.7470528353329418783e-461j)  +/-  (1.06e-116, 1.06e-116j)
| (-0.67622110738364370742 + 1.6778259488171590116e-468j)  +/-  (1.8e-119, 1.8e-119j)
| (-0.74545312710907243873 + 3.5181740431133592941e-468j)  +/-  (9.41e-119, 9.41e-119j)
| (0.049251467843978539347 + 4.0875223705762507316e-473j)  +/-  (3.01e-127, 3.01e-127j)
| (0.80729249465490804419 + 1.9272621994006619488e-476j)  +/-  (4.54e-118, 4.54e-118j)
| (0.74545312710907243873 - 2.5940170237532523834e-478j)  +/-  (9.77e-119, 9.77e-119j)
| (-0.97017665850723381607 + 6.3791151247007675448e-479j)  +/-  (1.08e-116, 1.08e-116j)
| (-0.80729249465490804419 + 9.0621442153919236818e-482j)  +/-  (4.27e-118, 4.27e-118j)
| (-0.3399810435848562648 - 3.0650263747052159698e-484j)  +/-  (1.58e-123, 1.58e-123j)
| (0.43132144608221740022 - 4.9554491049536378207e-482j)  +/-  (2.13e-122, 2.13e-122j)
| (0.67622110738364370742 + 6.4346054141404891566e-486j)  +/-  (1.79e-119, 1.79e-119j)
| (0.24525573475850863619 - 6.5684335026805762368e-490j)  +/-  (9.92e-125, 9.92e-125j)
| (-0.43132144608221740022 - 5.4782226967080943612e-492j)  +/-  (2.23e-122, 2.23e-122j)
| (-0.51837443977286981246 + 3.8679838364130767636e-495j)  +/-  (2.88e-121, 2.88e-121j)
| (-0.049251467843978539347 - 2.6607796743462495647e-496j)  +/-  (2.27e-127, 2.27e-127j)
| (0.60027798057116074735 + 7.7524193718870179471e-501j)  +/-  (2.35e-120, 2.35e-120j)
| (0.3399810435848562648 + 1.1048831422162456349e-502j)  +/-  (1.54e-123, 1.54e-123j)
| (-0.24525573475850863619 - 1.3208196008494930863e-503j)  +/-  (1.08e-124, 1.08e-124j)
| (-0.60027798057116074735 + 8.0319756991493984842e-503j)  +/-  (2.53e-120, 2.53e-120j)
| (-0.14807069785718442261 + 7.4471323454737486137e-505j)  +/-  (4.34e-126, 4.34e-126j)
| (0.14807069785718442261 + 4.2078004644461503716e-507j)  +/-  (3.6e-126, 3.6e-126j)
| (0.51837443977286981246 + 6.0480437370671395696e-509j)  +/-  (2.75e-121, 2.75e-121j)
-------------------------------------------------
The weights are:
| (0.013707825825567057094 - 1.4106099328055867697e-436j)  +/-  (1.33e-22, 2.25e-78j)
| (-0.0015087750657843914324 + 7.059045737983651859e-436j)  +/-  (7.83e-23, 1.33e-78j)
| (0.04966698717769290355 - 9.1428278243196635022e-438j)  +/-  (2.19e-23, 3.71e-79j)
| (0.031875619675026881734 - 5.8982416570998271062e-438j)  +/-  (1.68e-23, 2.86e-79j)
| (0.031875619675026881734 - 2.5074648594425571245e-436j)  +/-  (8.05e-24, 1.37e-79j)
| (0.040937952063156256137 + 1.7299137444660968231e-436j)  +/-  (5.66e-24, 9.6e-80j)
| (0.013707825825567057094 - 2.543913681511720859e-438j)  +/-  (5.77e-25, 9.8e-81j)
| (0.040937952063156256137 + 7.473254758459081749e-438j)  +/-  (9.46e-25, 1.61e-80j)
| (0.0055412770762262705745 + 8.1604246665828494636e-439j)  +/-  (3.25e-25, 5.51e-81j)
| (0.0055412770762262705745 - 1.6998578141496525826e-436j)  +/-  (4.91e-26, 8.33e-82j)
| (0.04966698717769290355 - 1.3294351327653052637e-436j)  +/-  (6.23e-27, 1.06e-82j)
| (0.022677392826629869643 + 4.6254265793112115086e-436j)  +/-  (9.78e-26, 1.66e-81j)
| (0.072707224366412453535 + 1.6237046255891293902e-437j)  +/-  (2.19e-28, 3.72e-84j)
| (0.065643070019151222185 - 1.3334514795542259148e-437j)  +/-  (4.15e-28, 7.04e-84j)
| (0.099640279007225884281 - 4.7149728240254633063e-436j)  +/-  (3.54e-29, 6e-85j)
| (0.057934990377728518702 + 1.09532256417456287e-436j)  +/-  (2.1e-28, 3.56e-84j)
| (0.065643070019151222185 - 9.518940336884356368e-437j)  +/-  (3.28e-29, 5.56e-85j)
| (0.022677392826629869643 + 4.2868713149320907534e-438j)  +/-  (4.92e-28, 8.35e-84j)
| (0.057934990377728518702 + 1.1043116625220778939e-437j)  +/-  (1.12e-28, 1.9e-84j)
| (0.093186005428914477328 + 4.6444329990684572987e-437j)  +/-  (1.52e-31, 2.57e-87j)
| (0.089344140654578913094 - 8.53205135043740135e-437j)  +/-  (1.01e-31, 1.72e-87j)
| (0.072707224366412453535 + 8.6596444639593878415e-437j)  +/-  (7.79e-31, 1.32e-86j)
| (0.096109672612969090286 - 1.1703876787544407673e-436j)  +/-  (8.09e-32, 1.37e-87j)
| (0.089344140654578913094 - 3.3475936857149222008e-437j)  +/-  (5.04e-32, 8.55e-88j)
| (0.084618002669987075545 + 2.5472997590949502327e-437j)  +/-  (4.61e-32, 7.82e-88j)
| (0.099640279007225884281 - 4.2673554676219316527e-436j)  +/-  (3.34e-32, 5.67e-88j)
| (0.079053767556056947712 - 8.2246368625674117984e-437j)  +/-  (4.85e-33, 8.22e-89j)
| (0.093186005428914477328 + 9.515339516230433785e-437j)  +/-  (3.84e-33, 6.53e-89j)
| (0.096109672612969090286 - 7.0500501019572567379e-437j)  +/-  (1.81e-33, 3.07e-89j)
| (0.079053767556056947712 - 2.009039204369341342e-437j)  +/-  (1.75e-33, 2.98e-89j)
| (0.098110180195568374314 + 1.2820235946298490809e-436j)  +/-  (1.66e-33, 2.81e-89j)
| (0.098110180195568374314 + 1.7338615833821542559e-436j)  +/-  (6.87e-34, 1.18e-89j)
| (0.084618002669987075545 + 8.1668105134827653654e-437j)  +/-  (1.28e-34, 2.08e-90j)
